17 research outputs found

    Planar three-loop QCD helicity amplitudes for VV+jet production at hadron colliders

    Full text link
    We compute the planar three-loop Quantum Chromodynamics (QCD) corrections to the helicity amplitudes involving a vector boson V=Z,W±,γV=Z,W^\pm,\gamma^*, two quarks and a gluon. These amplitudes are relevant to vector-boson-plus-jet production at hadron colliders and other precision QCD observables. The planar corrections encompass the leading colour factors N3N^3, N2NfN^2 N_f, NNf2N N_f^2 and Nf3N_f^3. We provide the finite remainders of the independent helicity amplitudes in terms of multiple polylogrithms, continued to all kinematic regions and in a form which is compact and lends itself to efficient numerical evaluation.Comment: 8 pages, 1 figure, 1 table, ancillary files are available https://xjetamps.hepforge.or

    Two-loop helicity amplitudes for H+H+jet production to higher orders in the dimensional regulator

    Full text link
    In view of the forthcoming High-Luminosity phase of the LHC, next-to-next-to-next-to-leading (N3^3LO) calculations for the most phenomenologically relevant processes become necessary. In this work, we take the first step towards this goal for H++jet production by computing the one- and two-loop helicity amplitudes for the two contributing processes, HgggH\to ggg, HqqˉgH\to q\bar{q}g, in an effective theory with infinite top quark mass, to higher orders in the dimensional regulator. We decompose the amplitude in scalar form factors related to the helicity amplitudes and in a new basis of tensorial structures. The form factors receive contributions from Feynman integrals which were reduced to a novel canonical basis of master integrals. We derive and solve a set of differential equations for these integrals in terms of Multiple Polylogarithms (MPLs) of two variables up to transcendental weight six.Comment: 32 pages; 3 figures, 3 tables; ancillary files with results in Mathematica forma

    Two-loop helicity amplitudes for V+V+jet production including axial vector couplings to higher orders in ϵ\epsilon

    Full text link
    We compute the two-loop Quantum Chromodynamics (QCD) corrections to all partonic channels relevant for the production of an electroweak boson V=Z,W±,γV=Z,W^\pm,\gamma^* and a jet at hadron colliders. We consider the decay of a vector boson VV to three partons Vqqˉg V \to q\bar{q}g, Vggg V \to ggg with a vector and axial vector coupling in both channels, including singlet and non-singlet contributions. For the quark channel, we use a recent tensor decomposition and extend the calculation to O(ϵ2)\mathcal{O}(\epsilon^2). For the gluonic channel, we define a new tensor decomposition which allows us to compute the vector and the axial vector amplitudes at once and to perform the computation of the amplitudes to O(ϵ2)\mathcal{O}(\epsilon^2). We provide finite remainders of the helicity amplitudes analytically continued to all relevant scattering regions qqˉVgq\bar{q} \to V g, qgVqq g \to V q and ggVggg \to V g. The axial vector contribution to the gluon-induced channel completes the set of two-loop amplitudes for this process, while the extension to O(ϵ2)\mathcal{O}(\epsilon^2) represents the first step in the calculation of next-to-next-to-next-to-leading-order (N3^3LO) QCD corrections to ZZ+jet production at hadron colliders.Comment: 28 pages. Ancillary files to this work are available at https://users.hepforge.org/~petr-jak/Vjet_2L.htm

    Two-loop non-planar hexa-box integrals with one massive leg

    Get PDF
    Based on the Simplified Differential Equations approach, we present results for the two-loop non-planar hexa-box families of master integrals. We introduce a new approach to obtain the boundary terms and establish a one-dimensional integral representation of the master integrals in terms of Generalised Polylogarithms, when the alphabet contains non-factorisable square roots. The results are relevant to the study of NNLO QCD corrections for W,ZW,Z and Higgs-boson production in association with two hadronic jets.Comment: Ancillary files attached. Mathematica notebook files updated. Accepted for publication in JHE

    Two-loop master integrals for a planar and a non-planar topology relevant for single top production

    No full text
    Abstract We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential Equations approach is employed for their analytic solution. The necessary boundary terms are computed in closed form in the dimensional regulator, allowing us to obtain analytic results in terms of multiple polylogarithms of arbitrary transcendental weight. We provide explicit solutions of all two-loop master integrals up to transcendental weight six and discuss their numerical evaluation for Euclidean and physical phase-space points

    Pentagon integrals to arbitrary order in the dimensional regulator

    Full text link
    We analytically calculate one-loop five-point Master Integrals, \textit{pentagon integrals}, with up to one off-shell leg to arbitrary order in the dimensional regulator in d=42ϵd=4-2\epsilon space-time dimensions. A pure basis of Master Integrals is constructed for the pentagon family with one off-shell leg, satisfying a single-variable canonical differential equation in the Simplified Differential Equations approach. The relevant boundary terms are given in closed form, including a hypergeometric function which can be expanded to arbitrary order in the dimensional regulator using the \texttt{Mathematica} package \texttt{HypExp}. Thus one can obtain solutions of the canonical differential equation in terms of Goncharov Polylogartihms of arbitrary transcendental weight. As a special limit of the one-mass pentagon family, we obtain a fully analytic result for the massless pentagon family in terms of pure and universally transcendental functions. For both families we provide explicit solutions in terms of Goncharov Polylogartihms up to weight four.Comment: 13 pages, ancillary files in GitHub link; revised manuscript, to appear in JHE

    Two-loop master integrals for a planar and a non-planar topology relevant for single top production

    Full text link
    We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential Equations approach is employed for their analytic solution. The necessary boundary terms are computed in closed form in the dimensional regulator, allowing us to obtain analytic results in terms of multiple polylogarithms of arbitrary transcendental weight. We provide explicit solutions of all two-loop master integrals up to transcendental weight six and discuss their numerical evaluation for Euclidean and physical phase-space points.Comment: v1: 22 pages, ancillary files attached and in this link https://github.com/nsyrrakos/SingleTop1mass.git; v2: Fixed minor typos and added numerical check with AMFlow, matches published version (JHEP)
    corecore